Before the Bengals, Cincinnati was home to two other teams, the Cincinnati Celts and the Cincinnati Reds. The Celts was a member of the American Professional Fooball Association in 1921. The Celts were 1-3-0 in their only season. The Reds were around for two years before folding and were a member of the Western Division of the NFL.
In 1937, the Bengals were formed as a member in the American Football League however the league folded after that season. The team continued to play without any league affiliation. They had three chances to play NFL teams, the Chicago Bears, who they beat, defeated the Pittsburgh Pirates, and tied the Chicago Cardinals. The team once again joined an new AFL, but this folded and another started which folded with the start of World War II.
In 1967, Paul Brown restarted professional football in Cincinnati in the modern-era AFL. Many suggested a mascot for the new team, however the fan favorite was Buckeyes, not Bengals. The owners decided to call them the Bengals as a link to the past and also to prevent confusion with the Ohio State Buckeyes. In 1970, the AFL merged with the NFL and the Bengals became a NFL team, where they remain to this day.
Information taken from www.bengals.com